valori initiale
consideram distanta d = 80 km
Timpul t
Viteza v
Dupa ce trenul este obligat sa stea la bariera, distanta ramane aceeasi dar se modifica timpul si viteza.
timpul devine t - 16 min = t-16/60 h =t- 4/15 h
iar viteza devine v+10.
80/v=80/(v+10)+4/15
80/v=(1200-4v-40)/(15v+150)
1200v+12000=1200v-4v²-40v
12000=-4v²-40v
4v²+40v-12000=0
v²+10v-3000=0
Δ=100+12000=12100
v₁=(-10+√12100)/2=(-10+110)/2=50
v₂=(-10-√12100)/2=(-10-110)/2=-60
(v+60)(v-50)=0
deci viteza prevazuta de orar=50 km/h
verificare
80 km : 50 km/h= 1,6 h
80 km :(50+10)km/h=1,(3) h
1,6-1,(3)=0,2(6) h
16 min = 16/60 h=0,2(6)h
